No, that's reductive BS. The GSA is an independent agency of the federal government:
[T]he term refers only to those independent agencies that, while considered part of the executive branch, have regulatory or rulemaking authority and are insulated from presidential control, usually because the president's power to dismiss the agency head or a member is limited.
Established through separate statutes passed by Congress, each respective statutory grant of authority defines the goals the agency must work towards, as well as what substantive areas, if any, over which it may have the power of rulemaking. These agency rules (or regulations), when in force, have the power of federal law.
The president DOES NOT have the power to fire people from this agency, nor change its rules without involving congress. Congress made this agency, and the president's job is to oversee its administration. Despite being the head of the executive branch, the president doesn't have direct authority over the GSA.
The president does. Who makes the laws (including the law creating this department)?